1/6 scale model prototyping

Let's see if I can ask my questions in a way that can be understood correctly: What does the boat speed with the speed of the wave and the wave length ?. Where do we put, in all this rigmarole, vessel length?

 

Let me try TANSL. I am a hobbyist though...

1. Wave speed and wave length relation was explained already. Big massive waves travel fast (that is why you need a jet ski to tow surfer to catch the giants).

2. Lots of things that happen to the boat are dependant on the waves it creates. For example often "hull speed" is explained with bow wave meeting stern wave or something like that. Basically the wave created by the boat itself at certain speed reaches a situation where the boat is going up hill due to its own wake. This is just an example of a situation where the speed of the boat and speed of a wave (and thus wave length) are linked.
So if you have a scale boat you need to understand that for simulating the same situation of the full size boat the wave speed must be calculated right. Said sqr rt comes at play here.

 

TANSL, the waves Tom and others have discussed are the waves created by the boat. The wave lengths are determined by the speed the boat is moving. The size and distribution of the waves is determined by the length of the boat relative to the wave length as well as the displacement and shape of the submerged part boat.

 

I still do not understand the statement : "Speed is scaled at square root of size ratio or 2.45." (I know that 2.45 is the square root of 6).
The energy of the wave created by the boat depends on the boat speed and displacement. That energy transmitted to the water generates a wave whose frequency does depend on the speed boat and whose length does depend on the length of the boat, but are not directly proportional. Another factor to consider is the height of the wave. Part of the energy transmitted by the ship spent on getting some wave height. All this leads me to guess that the length of the wave, the boat speed and length of the boat have a much more complex relationship than that expressed by the square root of the scale factor.
So simple, is what I think.
Returning to the initial questions of the OP, tom 28571 replied that "Speed is scaled at square root of size ratio or 2.45". Just wondering if this is correct because I found it a very simple formula and I wish I could understand it.
Thanks kerosene for your explanations.

 

Tansl, If you can get your hands on a copy of C.A. Marchajs book: Sailing Theory And Practice, you will find an eloquent explanation of wave theory as applied to boats. It is in the chapter of the book titled; The hydrodynamic resistance of the hull. The explanation about hull speed is made quite understandable in that chapter.

 

Thanks a lot messabout, I´ll try to get that book and re-read my old books on hydrodynamics, wave theory, etc.
I continue to think, however, the square root of 6 and why and how to get there.
I ask a stupid question: why the complicated calculations that are performed in the tank tests ?.
But I do not want to come to conclusions before having reviewed my knowledge on the subject.
Thank you all.